I think more specific information is needed to answer any particular questions regarding your situation. You likely need to consult with an immigration attorney and a tax attorney.
In general, if you are asking about an income tax refund, then you may be able to get such a refund by filing the appropriate tax forms in a timely manner. Presuming your card actually says "“VALID FOR WORK ONLY WITH DHS AUTHORIZATION” then if taxes are being withheld, you complete and file a tax return, and that return shows they owe you a refund, then yes you should be able to get a refund if you are otherwise eligible for the refund.
Information on this site is provided by Brian Scott Wayson as general information, not legal advice, and use of this information does not establish an attorney-client relationship. If you have questions about your specific situation, please call an attorney.
More facts are necessary to answer your question. A visit to a local tax professional to review your particular tax situation is suggested.
Any individual seeking legal advice for their own situation should retain their own legal counsel as this response provides information that is general in nature and not specific to any person's unique situation. Circular 230 Disclaimer - Advice given in this response cannot be used to eliminate penalties with the IRS or any other governmental agency.
The "Valid for work only" refers to the stamp on your SS Card that is palced there to show when you complete the I-9 for a new job the employer has to have proof from you that you have work authorization (ie a green card, or EAD card). As an employee you would be required to contribute through your wages to the SS program and if you stay long enough to become a US Citizen the wage credits for that time can be applied to your SS Retirement or if need be SS Disability credits. The only group of immigrants that do not contribute to SS through wages earned by employment is the H2A farmworkers who are 1099ed and by IRS regulation are exempt from employer contributions to Government programs FIT/FICA/SS
Legal disclaimer: The statement above is provided by CC Abbott is based on general assistance and not intended to be a legal opinion because not all the facts are provided. The person requesting information and all others reading the answer should retain an attorney who is permitted by the state bar within the jurisdiction who can examine the complete facts and provide a legal opinion on your case. All information provided in the above answer and other information provided by CC Abbott does not create an attorney/client relationship within any state of Federal law.